The grasping operation task in service scenes faces several problems including too many kinds of objects and a large amount of training data. This paper focuses on the grasping strategy and pose detection in desktop object grasping tasks. A grasping strategy is given based on the combination of desktop normal vector detection, object category detection, and grasping pose detection. The grasping pose is calculated by ellipse fitting on the depth map. An optimal function is designed to evaluate the possibility of the object sliding along the ellipse axis and the stability of the grasping height. The most reliable grasping pose is selected. Finally, experiments were carried out with a six-degree-of-freedom manipulator, and the proposed grasping method achieved effective grasping of desktop objects without prior knowledge of the object.